mathematics Article Prediction of Kerf Width in Laser Cutting of Thin Non-Oriented Electrical Steel Sheets Using Convolutional Neural Network Dinh-Tu Nguyen, Jeng-Rong Ho , Pi-Cheng Tung and Chih-Kuang Lin *   Citation: Nguyen, D.-T.; Ho, J.-R.; Tung, P.-C.; Lin, C.-K. Prediction of Kerf Width in Laser Cutting of Thin Non-Oriented Electrical Steel Sheets Using Convolutional Neural Network. Mathematics 2021, 9, 2261. https://doi.org/10.3390/math9182261 Academic Editor: Alessandro Niccolai Received: 25 August 2021 Accepted: 13 September 2021 Published: 15 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Department of Mechanical Engineering, National Central University, Jhong-Li District, Tao-Yuan City 32001, Taiwan; tu101074@gmail.com (D.-T.N.); jrho@ncu.edu.tw (J.-R.H.); t331166@ncu.edu.tw (P.-C.T.) * Correspondence: t330014@cc.ncu.edu.tw; Tel.: +886-3-4267-340 Abstract: Kerf width is one of the most important quality items in cutting of thin metallic sheets. The aim of this study was to develop a convolutional neural network (CNN) model for analysis and prediction of kerf width in laser cutting of thin non-oriented electrical steel sheets. Three input process parameters were considered, namely, laser power, cutting speed, and pulse frequency, while one output parameter, kerf width, was evaluated. In total, 40 sets of experimental data were obtained for development of the CNN model, including 36 sets for training with k-fold cross-validation and four sets for testing. Compared with a deep neural network (DNN) model and an extreme learning machine (ELM) model, the developed CNN model had the lowest mean absolute percentage error (MAPE) of 4.76% for the final test dataset in predicting kerf width. This indicates that the proposed CNN model is an appropriate model for kerf width prediction in laser cutting of thin non-oriented electrical steel sheets. Keywords: laser cutting; kerf width; convolutional neural network; non-oriented electrical steel 1. Introduction Non-oriented electrical steels are produced from Fe–Si or Fe–Si–Al alloys and used as the core material in electrical machinery [1]. Generally, the stator and rotor of electric motors are formed by lamination of non-oriented electrical steel sheets with a thickness of 0.1 mm to 1 mm. Such parts are usually stamped in a cost-effective way for mass production with limited precision. However, expensive fixtures and tools seem to be a drawback of stamping for low-volume production or rapid prototyping [2]. Laser cutting is an alternative to stamping, which could provide the availability to minimize the cost for small quantity production [2]. In addition, the plastic and elastic stresses induced by mechanical cutting could result in deterioration of the magnetic properties of electrical steel [3] and efficiency of the core [4–6]. Shear deformation at the cutting edge is typically found in conventional mechanical cutting processes, which might have a detrimental effect on the core performance in electrical machinery [7,8]. The magnetic field and flux density of electrical steels are affected by residual stress [9,10]. For laser cutting, no remarkable shear deformation at the cutting edge is found [11]. There are several process parameters influencing the kerf quality of laser cutting, including laser power, pulse frequency, and cutting speed. High-quality kerf of non- oriented electrical steel sheet is achievable with proper design of laser process parameters. Therefore, an investigation into the prediction of kerf width using various combinations of laser cutting process parameters is essential. Several methods have been proposed for kerf width prediction in laser cutting of metals [12–17]. Mathematical models [12–14] have been widely used to assess kerf quality for laser cutting processes. Statistical analysis has been conducted to study the effect of process parameters on the laser cutting quality [13,14]. Recently, the artificial intelligence (AI) technique has attracted more attention in effectively predicting the kerf quality of laser cutting [15,17]. Although there are a variety of AI Mathematics 2021, 9, 2261. https://doi.org/10.3390/math9182261 https://www.mdpi.com/journal/mathematics